What is the solution for y^{''}-y^'-2y=e^{-2t}-3e^{-t} ?

The solution for y^{''}-y^'-2y=e^{-2t}-3e^{-t} is y=c_{1}e^{2t}+c_{2}e^{-t}+1/4 e^{-2t}+e^{-t}t

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y^{''}-y^'-2y=e^{-2t}-3e^{-t}

y^{^{''}} - y^{^{'}} - 2 y = e^{- 2 t} - 3 e^{- t}

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{4} e^{- 2 t} + e^{- t} t

Solution steps

y^{''} (t) - y^{'} (t) - 2 y = e^{- 2 t} - 3 e^{- t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{4} e^{- 2 t} + e^{- t} t

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{4} e^{- 2 t} + e^{- t} t

What is the solution for y^{''}-y^'-2y=e^{-2t}-3e^{-t} ?
The solution for y^{''}-y^'-2y=e^{-2t}-3e^{-t} is y=c_{1}e^{2t}+c_{2}e^{-t}+1/4 e^{-2t}+e^{-t}t